CO(g) + 2 H2(g) ⇄ CH3OH(g) DH < 0 The synthesis of CH3OH(g) from CO(g) and H2(g) is represented by t — Equilibrium Chemistry Question

STEPS:

1. Analyze the thermodynamic sign of the enthalpy change ($\Delta H$): The given chemical equation is $\text{CO}(g) + 2\text{ H}_2(g) \rightleftharpoons \text{CH}_3\text{OH}(g)$ with $\Delta H < 0$. A negative enthalpy change ($\Delta H < 0$) indicates that the forward reaction is exothermic (it releases heat). We can conceptually write "heat" as a product on the right side of the equilibrium:
$$\text{CO}(g) + 2\text{ H}_2(g) \rightleftharpoons \text{CH}_3\text{OH}(g) + \text{heat}$$
2. Apply Le Chatelier's Principle to the temperature increase: When the temperature of the reaction system is increased (from $483\text{ K}$ to $650\text{ K}$), the system counteracts this stress by shifting in the direction that absorbs heat (the endothermic direction). Since the forward reaction is exothermic, the reverse reaction is endothermic. Therefore, the equilibrium will shift to the left (toward the reactants).
3. Relate the equilibrium shift to the equilibrium constant expression ($K_c$): The equilibrium constant expression for this reaction is:
$$K_c = \frac{[\text{CH}_3\text{OH}]}{[\text{CO}][\text{H}_2]^2}$$
Because the system shifts to the left, the concentration of the product ($\text{CH}_3\text{OH}$) decreases while the concentrations of the reactants ($\text{CO}$ and $\text{H}_2$) increase. Mathematically, a decrease in the numerator accompanied by an increase in the denominator results in a smaller value of $K_c$.
4. Identify the underlying chemistry concept (Temperature Dependence of $K$): The value of an equilibrium constant $K$ depends solely on temperature. For any exothermic reaction, raising the temperature favors the reactants and causes the equilibrium constant to decrease. This explains why $K_c$ at $650\text{ K}$ will be less than the value of $14.5$ measured at $483\text{ K}$, making Option C the correct answer.

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WHY_OTHERS_WRONG:

• A is incorrect: The activation energy ($E_a$) of a reaction is a fixed barrier determined by the reaction pathway and does not increase when temperature increases. While a temperature increase provides molecules with more kinetic energy to overcome the activation barrier, it does not alter the value of $E_a$ itself.
• B is incorrect: The difference in the number of reactant molecules (3 moles of gas) versus product molecules (1 mole of gas) determines how the system responds to a change in volume or pressure (according to Le Chatelier's Principle), not temperature. This structural detail has no bearing on how temperature shifts the value of $K_c$.
• D is incorrect: The equilibrium constant is only constant if the temperature remains constant. Because chemical equilibrium is a temperature-dependent state, changing the temperature must change the value of $K_c$.